Question: Kevin is 4 years older than William. For the last two years, Kevin and William have been going to the same school. Fifteen years ago, Kevin was 5 times older than William. How old is Kevin now?
Solution: We can use the given information to write down two equations that describe the ages of Kevin and William. Let Kevin's current age be $k$ and William's current age be $w$ The information in the first sentence can be expressed in the following equation: $k = w + 4$ Fifteen years ago, Kevin was $k - 15$ years old, and William was $w - 15$ years old. The information in the second sentence can be expressed in the following equation: $k - 15 = 5(w - 15)$ Now we have two independent equations, and we can solve for our two unknowns. Because we are looking for $k$ , it might be easiest to solve our first equation for $w$ and substitute it into our second equation. Solving our first equation for $w$ , we get: $w = k - 4$ . Substituting this into our second equation, we get the equation: $k - 15 = 5($ $(k - 4)$ $ -$ $ 15)$ which combines the information about $k$ from both of our original equations. Simplifying the right side of this equation, we get: $k - 15 = 5k - 95$ Solving for $k$ , we get: $4 k = 80$ $k = 20$.